The previous mark was a 13.6 rating, set Sept. 26, 2014, when the Royals clinched a playoff spot in a game against the White Sox.
Sunday's rating peaked at 19.4 (a 38 share) during an eighth-inning rally that saw the Royals score three runs to take the lead in an eventual 4-2 victory.
The weekend series averaged at 12.9, making it the highest-rated series ever on FOX Sports Kansas City.
Also, Sunday's "Boulevard Royals Live" postgame show drew an 8.2 rating, its highest ever.
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.